The Course aims to present some mathematical models for Architecture and implement their simulation on a computer, using numerical methods. To this end, this course involves two separate parts.
- The first part is devoted to NUMERICAL ANALYSIS and its purpose is to help understanding of theoretical and numerical mathematical tools used in modelling problems of interest for Architecture; programming language MATLAB is used for it is very user-friendly within this context of simple numerical computations. The presented topics are the following:
- Numerical solution of linear systems (systems of large order included) and their application to trusses.
- Interpolation of discrete data, with application to statistical data by public data set.
- Numerical methods for computing areas of general shapes and estimation of convergence errors and convergence rates for generalized methods.
- Numerical computation of volumes under surfaces with analytical expression and rotation volumes and surfaces.
- Numerical methods for solving ordinary differential equations, in particular modelling v building vibrations due to earthquakes.
- The second part of the course is called STRUCTURAL MODELLING FOR ARCHITECTURE: it aims to guide the student to the comprehension and to first use of a common Computer Aided Engineering (CAE) program for structural analysis. In particular, the following objectives are pursed.
- Reminder of continuum and elasticity theory in small strains/displacements; matrix (Voight’s) formulation.
- Minimum total potential energy (TPE) theorem, applied to discrete systems and to continua, to set the basis of the finite element (FE) method.
- Typologies of Fes used for structural problems (beams, trusses, shells, plates, 2D and 3D solid elements); reminder of interpolation methods (seen in part 1), convergence study.
- Description of the working rationale for one or more FE codes; common errors in structural modelling.
- Through practical, interactive work in the classroom, development of a first structural model for a specific problem addressed by each student in an architectural design, urbanistic, internal design laboratory course that takes places at the same time or an alternative significant model.
References will be provided during the course.